The breakup of river ice covers is commonly initiated by the formation of cracks parallel to river banks. These cracks usually result from a change in the water level due to a rapid rising of river discharge. Analytical models have been previously developed to predict such phenomena to a limited extent. Numerical approaches being currently developed for modelling the hydrodynamic-structural interaction leading to initiation of cracks are presented. Modelling processes assuming elastic behavior of the ice, are based on the finite element stiffness method which has been used to develop the FEM1 Model. The formulation of FEM1 is based on theoretical behavior of a beam on an elastic foundation. The FEM1 Model is a versatile model to predict the initiation of longitudinal cracks for river ice covers. The prediction of crack position is based on the existing combination of bending moment and shearing forces in the ice cover and employs the theory of principal stresses for locating failure. The model is capable of examining different river types (i.e. narrow, medium, and wide), various types of boundary conditions and uniform or nonuniform ice covers, including haunched parts near the banks.